The number of turns in a solenoid is doubled, and at the same time its length is

Question

The number of turns in a solenoid is doubled, and at the same time its length is doubled. Does the magnetic field within the solenoid increase, decrease, or stay the same? Choose the best explanation from among the following: Making a solenoid longer decreases its magnetic field, and therefore the field decreases The magnetic field remains the same because the number of turns per length is unchanged. Doubling the number of turns in a solenoid doubles its magnetic field, and hence the field increases.

Explanation / Answer

B = 0IN/L

Where B0= magnetic field

0 = permeability of free space

I= current

N= no of turns

L= length of the solenoid

A) From above equation,

B1 = 0IN1/L1

B2 = 0IN2/L2

B2/B1= N2L1/N1L2

When N2=2N1 and L2=2L1

B2=B1*(2N1L1)/(N1*2L1) = B1

Thus

Magnetic field remains same.

B) The magnetic field remains same because the number of turns per length (n=N/L) is unchanged.

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